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Math  /  Algebra

Question6.) Evaluate the following expression: −a+12b+4c-a+12 b+4 c if a=−3−3b=1/4a=-3-3 \quad b=1 / 4 and c=−c=- A. 10 −+(12×1/4)+(4x−4)=12×14=12/44x−4=−16\begin{aligned} - & +(12 \times 1 / 4)+(4 x-4)= \\ & 12 \times \frac{1}{4}=12 / 4 \\ 4 x-4 & =-16 \end{aligned} B. -10 4x−4=−164 x-4=-16 C. -16 D. 16

Studdy Solution

STEP 1

1. We need to evaluate the expression −a+12b+4c-a + 12b + 4c.
2. The given values are a=−3a = -3, b=14b = \frac{1}{4}, and c=−4c = -4.
3. We are to determine which of the multiple-choice options (A. 10, B. -10, C. -16, D. 16) is correct.

STEP 2

1. Substitute the given values into the expression.
2. Simplify the expression step by step.
3. Compare the result with the multiple-choice options.

STEP 3

Substitute the given values into the expression −a+12b+4c-a + 12b + 4c.
Given: a=−3a = -3, b=14b = \frac{1}{4}, c=−4c = -4
Substitute: −a+12b+4c=−(−3)+12(14)+4(−4)-a + 12b + 4c = -(-3) + 12\left(\frac{1}{4}\right) + 4(-4)

STEP 4

Simplify the expression step by step.
First, simplify −(−3)-(-3): −a=3-a = 3
Next, calculate 12×1412 \times \frac{1}{4}: 12b=12×14=312b = 12 \times \frac{1}{4} = 3
Then, calculate 4×(−4)4 \times (-4): 4c=4×(−4)=−164c = 4 \times (-4) = -16
Combine all parts: 3+3−163 + 3 - 16

STEP 5

Continue simplifying:
Add 3+33 + 3: 6−166 - 16
Subtract: 6−16=−106 - 16 = -10

STEP 6

Compare the result with the multiple-choice options.
The result is −10-10, which corresponds to option B.
The correct answer is −10\boxed{-10}.

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